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Chapter 7: Q. 25 (page 178)

The $100 k g$ block in FIGURE EX $7.25$ takes $6.0 s$ to reach the floor after being released from rest. What is the mass of the block on the left? The pulley is massless and frictionless.

Short Answer

Expert verified

The acceleration of the $2.0 k g$ blocks is $2.16 m / s^{2}$

Step by step solution

01

Given information

Mass of right block, $M = 100 k g$

Time taken $t = 6 s$

Distance moved $s = 1 m$

02

Explanation

Equation of motion for mass m

$T - m g = m a 鈥� 鈥� (1)$

Equation of motion for mass M:

$M g - T = M a 鈰� 鈰� (2)$

On adding equation $(1) and(2)$

$g (M - m) = a (M + m) m = \frac{M (g - a)}{(g + a)}$

Acceleration a can be calculated as follows.

localid="1649613906426" $s = u t + \frac{1}{2} a t^{2} u = 0 s = 1 m t = 6 s 1 m = 0 + \frac{1}{2} (a) {(6 s)}^{2} a = \frac{2}{36} m / s^{2} a = 0.055 m / s^{2} m = \frac{(100 k g) (9.8 m / s^{2} - 0.055 m / s^{2})}{(9.8 m / s^{2}) + (0.055 m / s^{2})} m = 98.87 k g$

The mass of the block on the left side is $98.87 k g$

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Most popular questions from this chapter

The century-old ascensores in Valparaiso, Chile, are picturesque cable cars built on stilts to keep the passenger compartments level as they go up and down the steep hillsides. As FIGURE P $7.43$ shows, one car ascends as the other descends. The cars use a two-cable arrangement to compensate for friction; one cable passing around a large pulley connects the cars, the second is pulled by a small motor. Suppose the mass of both cars (with passengers) is $1500 k g$ , the coefficient of rolling friction is $0.020$ , and the cars move at constant speed. What is the tension in (a) the connecting cable and (b) the cable to the motor?

Teams red and blue are having a tug-of-war. According to Newton鈥檚 third law, the force with which the red team pulls on the blue team exactly equals the force with which the blue team pulls on the red team. How can one team ever win? Explain

Will hanging a magnet in front of the iron cart in the given figure make it go? Explain.

$F I G U R E C P 7.58$ shows three hanging masses connected by massless strings over two massless, frictionless pulleys.

a. Find the acceleration constraint for this system. It is a single equation relatinglocalid="1649865348893" $a_{1 y}, a_{2 y}, a n d a_{3 y} .$ Hint: $y_{A}$ isn鈥檛 constant.

b. Find an expression for the tension in string $A .$ Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns.

c. Suppose: $m_{1} = 2.5 k g, m_{2} = 1.5 k g, a n d m_{3} = 4.0 k g .$ Find the acceleration of each.

d. The $4.0 k g$ mass would appear to be in equilibrium. Explain why it accelerates.

The $1.0 k g$ physics book in FIGURE P $7.41$ is connected by a string to a $500 g$ coffee cup. The book is given a push up the slope and released with a speed of $3.0 m / s$ . The coefficients of friction are $渭_{s} = 0.50$ and $渭_{k} = 0.20$

a. How far does the book slide?

b. At the highest point, does the book stick to the slope, or does it slide back down?

See all solutions

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